I feel like I forgot my simple mathematical knowledge

Question

Please help me. I can not tell psychologists about this because they are not mathematicians (They will not understand me)

Sometimes I don't read about mathematics for a couple of months, I do not think anything about my research and then I feel like I forget everything when I go back to research.

For example, I was working on a very important problem in March, and then I stopped doing mathematics so far. I want to go back to my research now, but I feel myself as weak, exhausted, lost my math skills and charlatan. Fear of failure, fear of losing everything, makes me crazy.

what can I do?

When I start researching again I have to learn math from scratch because I feel I have forgotten everything. It's disgusting because it makes me feel bad.

Please give advice =)

Thanks

Answer 1

As a grad student in computer engineering, I have a similar problem when I switch between projects that use different programming languages. I might spend months working in a high-level language like Python, only to switch to a project using a low-level language like C, or a project whose language I'm unfamiliar with, like MATLAB.

As I see it, there are two issues here:

1. Documentation -- setting a project aside is unavoidable at some point. As @Bemte pointed out, the trick is to document your work well enough where you can pick the train of thought back up days, weeks, or months later. This takes time and effort to do well (something I'm still learning). Suffice to say -- your documentation should include everything that you need to familiar with the work in a reasonable amount of time. That might include:

• Detailed notes of the conversations you had, proofs you were working on, etc.
• Papers you were reading
• Textbook chapters that are important
• And so on.

2. Patience -- you said it's been a couple of months since you had looked at your work. I can say for sure that if I went 2 or 3 months without looking at my code, it would be like reading gibberish, and it would take me a couple of weeks minimum to get back up to full productivity. I may be reading too far into your words, but it sounds to me that you need to be patient with yourself. High-level mathematics is not a subject that you learn overnight; and any psychologist will tell you that it takes time to enter the flow. Be patient with yourself.

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I'll add this quick caveat: if you're concerned that you're still forgetting information even after you've been working on it continuously for weeks/months, that may be a sign of a more significant neurological or mental health problem. In that case, consult with (medical) experts. (Update: see @aparente001's excellent answer on how to best do this here.)

But otherwise, it's likely just a matter of being human -- we all forget things after a while :)

Answer 2

Others have contributed helpful things, e.g. make notes before putting a project on a back burner. But I want to tell you about something that I haven't seen here yet. I don't know whether this will be relevant for you; but it might be, so here goes.

I help my fourteen-year-old son with his math when he needs help. He's taking Algebra this year. What I see is that there are periods, which sometimes last several weeks, in which he seems to have forgotten everything he ever knew about math!

He has some neurological differences, specifically, Tourette Syndrome, ADHD, OCD and anxiety. Of all of those, the one that I have been able to trace most clearly to these periods of difficulty functioning in math is... (drumroll please)... anxiety.

I know nothing about you. I have no idea if anyone would find any neurological differences or mental health issues that might explain what you have experienced. But what I can tell you is how to find out.

The place to start is with your general practitioner (primary medical provider), and the next step is to get what's called a psychoeducational evaluation. This can be covered by health insurance if it is ordered by your primary provider.

When you go see the doctor, just print out the question you posted here and give it to him or her.

Answer 3

Sounds very much like the thing psychologists would know all about. That it happens specifically with mathematics is hardly relevant from the sound of it. I suggest disabusing yourself of the idea that being a mathematician makes you some sort of incomprehensible, special snowflake. You might need to specifically look for someone who has experience and specialties working with professionals or even academics, but beyond that you are definitely understandable enough to be helped.

You show some, in my opinion, strong indicators of having fairly common psychological issues that a professional might be of great help to you with. Feelings of inadequacy and failure are quite common among researchers and other (high-end) professionals, and the more they dictate your life and well-being the more you should seek help. And altering the nature of your life and how you view yourself for months at a time is pretty significant.

That said, there is an academia-specific matter that can be addressed here.

As others have mentioned, being patient with yourself (it's hardly unusual to find your own work alien when you've not touched it in months) and documenting your work better are great ideas. There are also a couple of standard approaches researchers can use to keep themselves fresh even when they can't stay laser-focused on something.

• The Feynman approach, as I'll call it, since this is something he specifically did for much the same reasons I'll state: teach. Teaching courses, be they undergraduate or graduate, helps keep you connected with the basic idea of doing math/physics/whatever, even if it's at a fairly elementary level. It's also great for forcing you to do rote repetition learning. You might be surprised at how much you help yourself by teaching courses. Constantly drilling in the basics of group theory, ring theory, even calculus is extremely useful for having the masteries of the fundamentals necessary to do good research. Teaching the occasional advanced topics course is also good. This can fix your issue with feeling like you're forgetting fundamentals pretty quickly.

• Have a backup plan. Don't overspecialize by only ever having one thing to research and think about. Have a few other things on the back burner, so that when you're bored with idea A, or it's evolved to a high-effort enterprise you can't afford right now, you can switch over to one of B, C, or D. I keep a list of all of the research ideas I think up, so I can consult it whenever I need something. Don't be afraid or ashamed if some of the projects seem silly or minor. To steal and modify a line from Star Trek: Don't try to be a great mathematician. Just be a mathematician, and let history make its own judgments. Sometimes greatness emerges from amusing little dalliances. But most importantly, fun and amusement routinely do.

• Socialize. Even if you can't teach, or can't seem to find anything to research even in a playful sort of way, there are still options. Attending conferences, or seminars at local universities (your own or not), are simple, low-intensity ways of keeping yourself engaged and (technically) productive without actually requiring you to produce novel new research. Giving talks can also help, and doing so doesn't always require you to have novel new results—sometimes a survey of results in a field, or a discussion of preliminary results, is acceptable or straight-up desirable. Attending such events also makes it easier to pick up additional topics for research, or people who will collaborate with you. This can turn a project that you couldn't proceed with into one that you can, should they luckily be interested in it. You'll also better understand your place in the research community. Because, quite honestly, some talks are awful. And realizing that there are successful researchers that sometimes (or often) give talks that bomb or are just plain boring and opaque can be reassuring. Be courteous to the speaker, of course, but take solace that the occasional failure or misstep is hardly a problem only you suffer from.

Answer 4

• When documenting your progress, err on the side of leaving a bit too much detail or explanation. This will increase the amount of time you can pick up and understand a document.

• You might be experiencing Impostor syndrome, in which case, remember to "fake it 'til you make it".

Answer 5

Mathematics, anxiety, and the brain
This info is from the NCBI, I am constructing it from the Abstract:
Studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. This paper discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. It also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia).

It says that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Hope this help.